Optimal critical mass for the two-dimensional keller-segel model with rotational flux terms

Elio Espejo, Hao Wu

Research output: Journal PublicationArticlepeer-review

Abstract

Our aim is to show that several important systems of partial differential equations arising in mathematical biology, fluid dynamics and electrokinetics can be approached within a single model, namely, a Keller-Segel-type system with rotational flux terms. In particular, we establish sharp conditions on the optimal critical mass for having global existence and finite time blow-up of solutions in two spatial dimensions. Our results imply that the rotated chemotactic response can delay or even avoid the blow-up. The key observation is that for any angle of rotation α∈(-π, π], the resulting PDE system preserves a dissipative energy structure. Inspired by this property, we also provide an alternative derivation of the general system via an energetic variational approach.

Original languageEnglish
Pages (from-to)379-394
Number of pages16
JournalCommunications in Mathematical Sciences
Volume18
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Blow-up
  • Chemotaxis
  • Critical mass
  • Dissipative energy structure
  • Global existence
  • Rotational flux

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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